Modelling urban air pollution Id
-33y (j^xc- / 0
Almosfheric Knriron'M'nt Vol. 8. pp. 555-561. Pcrgamon Press 1974. Printed in Great Britain.
AIM .Rejected
MODELLING URBAN AIR POLLUTION
' '
S. HAMEED
.. Institute for Space Studies, NASA, New York, New York 10025, U.S.A.
(First received 13 April 1973 and in final form 22 November 1973)
Abstract—The performance of simple, one parameter, models for predicting dispersion of air pollutants in urban atmospheres is compared with that of more sophisticated methods. It is concluded
that presently available simple models are not dependable enough to preclude the development
of more complex models.
1. I N T R O D U C T I O N
Si
§2i
sa\
H
SO
In recent years a number of models have been developed to predict the dispersion of contaminants in urban atmospheres. These models range in complexity from those designed to
solve the three-dimensional diffusion equation to models containing only one parameter.
In this paper we compare the performance of some theoretical models of varying complexity and draw conclusions about their suitability. These calculations predict the dispersion
of SO2 during a period of 2 h (16:00 - 18:00 CST) on 11 January 1959 in the atmosphere
of Nashville, Tennessee, a city for which more than usual amount of relevant data are
available.
2. C O M P A R I S O N
Randcrson (1968, 1970) approached this problem by numerically solving the three
dimensional diffusion equation, including the effects of horizontal and vertical advection
and chemical decay, thus predicting the evolution of the concentration pattern of SO2 for
the 2-h period. Halliday and Ventner (1971) have criticised this calculation by suggesting
that concentration values, X, obtained by the simple formula
O
O
X
V
S\I
X
= Q/u
*:
'
'
' '
/t \
(1)
' '
Ul
ui a
LJ O
LJ O
fs M
CO (U
Si
^1
CD
I
•-J
VO
ON
where Q is the local source strength and u the mean wind speed, are as good as those of
the detailed model of Randerson. Gifford and Hanna (1973) have invoked the argument
of Halliday and Ventner in support of their own model according to which,
•-••
'
. ; .
' '•
\
-
X-cQ/u,
-'••
where the constant of proportionality c is
'
'
x,
...
/"W^J/Z ~ ( l - f c ) r w t
J.VI"1
.:
'
.
•
(2)
....,...._.
•
' il\
c = \£/ii) x
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o
.52
'33
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Modelling urban air pollution
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558
S. HAMKED
For further comparison we present also in Table 1 the results obtained for the same
problem by the use of a multi-cell model. (Hameed. 1974). In this method the area under
study is divided into control volumes, or cells, of 1 mile 2 each. In each of these cells pollutant concentration is assumed to be horizontally uniform and to have a Gaussian distribution in the vertical direction. This calculation neglects the effects of horizontal turbulent
diffusion and those of chemical decay. It is intermediate in complexity between the comprehensive and very simple models discussed above.
3. I N D I C E S FOR GOODNESS OF P R E D I C T I O N
In the bottom two rows of Table 1 we present, for each calculation, the correlation coefficient and the mean relative error. It may be noted that the correlation coefficient, being
independent of an arbitrary multiplicative factor in either of the sets of numbers being
studied, is not, by itself, a sufficiently transparent index for indicating the success of a prediction. It is important to consider also a measure of relative magnitudes, such as the mean
relative error. For instance, although the correlation coefficients of Randerson's numerical
model and Gifford and Hanna's model are comparable, their relative mean errors are very
different, being —0.53 and 4.5 respectively. They show that, on the average, values predicted by Randerson's calculation are nearly 1/2 those of the observed ones, while the predictions of Gifford and Hanna model are, on the average, 5.5 times the observations.
An objective method of judging the predictive skill of a model is to test its performance
against a persistence forecast, which in the present case is given in column (8) of Table
1. If the proposed model cannot forecast the specified parameters better than persistence
then the model is of questionable value. Table 1 shows that in terms of the correlation
coefficient, persistence outperforms all the models considered, while in terms of the relative error, the multi-cell model appears to be the best. In fact the relevance of the initial
values of concentration with respect to the simple models is not clear. Under steady-state
conditions persistence is likely to be a good forecast. One could make a post facto calculation of the constant c in equation (2) based on the known initial conditions. Such a procedure would yield impressive values of the correlation coefficient and the mean relative
error, but these values would only be as good as a persistence forecast, not better.
4. F U R T H E R S I M P L I F I C A T I O N
Gifford and Hanna (1973) have introduced a further simplification of their model. They
have tabulated, the total annual pollutant emissions, annual average wind velocities, the
annual average pollutant concentrations and the areas for many cities in the United States.
Assuming that these data should conform to their model, i.e. equation (2), they have computed the constant c for each of the cities from the tabulated values of A', Q and ti. They
then have averaged over these values of c and proposed that equation (2), with the resulting
value of c, gives a general model for predicting urban air pollution. They have carried out
this procedure for two types of pollutants, oxides of sulfur (SOJ and paniculate matter.
Oxides of sulfur
For SOX the resulting equation obtained from data for 20 cities is:
X = 5QQfungm~ 3 .
(4)
The correlation coefficient between A' and Q/u for these 20 cities is 0.15. Now, if two
variables are totally uncorrelated. the probability that a random sample of 20 observations
560
S. HAMI-:KI>
Table 2. Comparison of three formulas, equations (5, 6 and 7X for predicting annual
average paniculate concentration in 29 U.S. cities
Index
Formula
X = 225 Q/u, equation (5)
X = 94 + 22 Q/u. equation (6)
(least squares fit)
X = 11 1, equation (7)
(average value)
Mean relative
error
Standard error
of estimate
0.56
124
0.06
26
0.07
29
5. C O N C L U S I O N S
Generally speaking, the case of Nashville discussed above illustrates that, at least in
some cases, urban air pollution modelling is a complex forecasting problem and simple
considerations like those of equations (1 and 2) are not sufficient to cope with it. As Gifford
and Hanna point out, most current detailed models of urban air pollution predict concentrations with errors, on the average, of the order of a factor of 2. This is because of
the poor quality of data and also because dispersion modelling is still a developing technique. Most of currently available data are such that a prediction better than with an error
of a factor of 2 may be regarded as fortuitous. This does not mean, however, that there
is no need for developing models which take account of the complexities of meteorological,
topographical or of other types, which determine the dispersion of pollutants. If dispersion modelling is to play a useful role in urban planning or in devising pollution control
strategies, it is necessary that reliable models of atmospheric dispersion be available. While
a sophisticated model developed for a particular situation can be depended upon to predict pollution concentration to within a factor of, say. 2 on the average, it is apparent from
considerations discussed above that simple models like equations (1 and 2) or (5) cannot
be relied upon to give results which are always co-rect to within a given margin of error.
Accuracy of detailed dispersion models is likely to increase as more and better data
become available. Moreover, a comprehensive dispersion model for a given location need
to be constructed only once, after which it can be used continuously with updated source
information and a predicted flow field to monitor and simulate the expected pollution
field. It is of course possible that under certain conditions simple models may give results
comparable to more sophisticated methods, but until such conditions are clearly understood and categorized one cannot depend upon the simple models.
Acknowledgements—The author wishes to thank Dr. D. Randerson of the Air Resources Laboratory of the U.S.
Department of Commerce for very useful discussions about this work.
"
#t** G****- /S*f.
33-
REFERENCES
Bevington P. R. (1969) Data Reduction and Error Analysis for the Physical Sciences, pp. 310-312. McGraw-Hill,
New York.
Gifford F. A. and Hanna S. R. (197!) Urban air pollution modelling. Proceedings of The 2nd International Clean
Air Congress (Edited by Englund H. M. and Beery \V. T.). pp. 1146-1151.
Gilford F. A. and Hanna S. R. (1973) Modelling urban air pollution. Atmospheric Environment 7, 131-136.
Halliday E. C. and Ventner G. (1971) A numerical experiment in simulating the transport of sulfur dioxide
thrnueh the atmosphere. Atmospheric Environment 5, 815-8IS.
Hamced S. (1974) A multi-cell method for simulation of atmospheric transport. Atmospheric Environment, to be
published.
Modelling urban air pollution
1
-4
S61
Miller M. E. and Holzworth G. C. (1967) An atmospheric diffusion model for metropolitan areas. J. Air Pollut.
Control Ass. 17,46-50.
Randerson D. (1968) A numerical model for predicting the transport of sulfur dioxide through the atmosphere.
Ph.D. dissertation, Texas A & M University, 153 pp.
Randerson D. (1970) A numerical experiment in simulating the transport of sulfur dioxide through the atmosphere. Almosplieric Environment 4, 615-632.
Smith M. (1961) The concentrations and residence times of pollutants in the atmosphere. Chemical Reactions
in the Lower and Upper Atmosphere, pp. 155-166. Interscience, New York.
Stalker W.W.. Kenline P: A. and Paulus H. J.( 1964) Nashville sulfurdioxide emission inventory and the relationship to measured sulfur dioxide. J. Air Pollut. Control Ass. 14, 469-474.
Almosfheric Knriron'M'nt Vol. 8. pp. 555-561. Pcrgamon Press 1974. Printed in Great Britain.
AIM .Rejected
MODELLING URBAN AIR POLLUTION
' '
S. HAMEED
.. Institute for Space Studies, NASA, New York, New York 10025, U.S.A.
(First received 13 April 1973 and in final form 22 November 1973)
Abstract—The performance of simple, one parameter, models for predicting dispersion of air pollutants in urban atmospheres is compared with that of more sophisticated methods. It is concluded
that presently available simple models are not dependable enough to preclude the development
of more complex models.
1. I N T R O D U C T I O N
Si
§2i
sa\
H
SO
In recent years a number of models have been developed to predict the dispersion of contaminants in urban atmospheres. These models range in complexity from those designed to
solve the three-dimensional diffusion equation to models containing only one parameter.
In this paper we compare the performance of some theoretical models of varying complexity and draw conclusions about their suitability. These calculations predict the dispersion
of SO2 during a period of 2 h (16:00 - 18:00 CST) on 11 January 1959 in the atmosphere
of Nashville, Tennessee, a city for which more than usual amount of relevant data are
available.
2. C O M P A R I S O N
Randcrson (1968, 1970) approached this problem by numerically solving the three
dimensional diffusion equation, including the effects of horizontal and vertical advection
and chemical decay, thus predicting the evolution of the concentration pattern of SO2 for
the 2-h period. Halliday and Ventner (1971) have criticised this calculation by suggesting
that concentration values, X, obtained by the simple formula
O
O
X
V
S\I
X
= Q/u
*:
'
'
' '
/t \
(1)
' '
Ul
ui a
LJ O
LJ O
fs M
CO (U
Si
^1
CD
I
•-J
VO
ON
where Q is the local source strength and u the mean wind speed, are as good as those of
the detailed model of Randerson. Gifford and Hanna (1973) have invoked the argument
of Halliday and Ventner in support of their own model according to which,
•-••
'
. ; .
' '•
\
-
X-cQ/u,
-'••
where the constant of proportionality c is
'
'
x,
...
/"W^J/Z ~ ( l - f c ) r w t
J.VI"1
.:
'
.
•
(2)
....,...._.
•
' il\
c = \£/ii) x
!_"
o
.52
'33
A
1
b
>ij
--".'tji
o
0
:
-•^.^
Iso
W
*
'
"= E
5
E
_
•V^
*.H|
— -o
•gis
§ la
t>
;•'.'.££
iJT'v!
S
£
:^l
•Ssp
ill
S
Ai^i
^ '=^5
.."*3
s^ ^
' '•
O
,-i
,^^
*s
7
o
I6
1b
•'.-•a '>i
fjjg|
2 *t3 ">
Hi
ssM"!
-ff»i\
:
.j'&
« 'i
«n
< N ^ O N —' O ^ ^ ^ J r
«NCS — o ^ t f ^ — r-o\
ooooociooo
•., 3
* ou
S C
•jj^(« ra
^>
*;Cr
>V'*;
J;~j
;.--^
'-..•^*^
^*? j
y®|
S
*:S
i%4
« •?
Z
CT
U
c -2
'" E
0
O"-§.
o.
fi —
H
^51
•M
-Jj
i- "'"'•i
•
Modelling urban air pollution
"°£
*i«38
;:;f|
•.-.
Ox
f^*n*O*oO
— oo
^- »n
oo^as o
558
S. HAMKED
For further comparison we present also in Table 1 the results obtained for the same
problem by the use of a multi-cell model. (Hameed. 1974). In this method the area under
study is divided into control volumes, or cells, of 1 mile 2 each. In each of these cells pollutant concentration is assumed to be horizontally uniform and to have a Gaussian distribution in the vertical direction. This calculation neglects the effects of horizontal turbulent
diffusion and those of chemical decay. It is intermediate in complexity between the comprehensive and very simple models discussed above.
3. I N D I C E S FOR GOODNESS OF P R E D I C T I O N
In the bottom two rows of Table 1 we present, for each calculation, the correlation coefficient and the mean relative error. It may be noted that the correlation coefficient, being
independent of an arbitrary multiplicative factor in either of the sets of numbers being
studied, is not, by itself, a sufficiently transparent index for indicating the success of a prediction. It is important to consider also a measure of relative magnitudes, such as the mean
relative error. For instance, although the correlation coefficients of Randerson's numerical
model and Gifford and Hanna's model are comparable, their relative mean errors are very
different, being —0.53 and 4.5 respectively. They show that, on the average, values predicted by Randerson's calculation are nearly 1/2 those of the observed ones, while the predictions of Gifford and Hanna model are, on the average, 5.5 times the observations.
An objective method of judging the predictive skill of a model is to test its performance
against a persistence forecast, which in the present case is given in column (8) of Table
1. If the proposed model cannot forecast the specified parameters better than persistence
then the model is of questionable value. Table 1 shows that in terms of the correlation
coefficient, persistence outperforms all the models considered, while in terms of the relative error, the multi-cell model appears to be the best. In fact the relevance of the initial
values of concentration with respect to the simple models is not clear. Under steady-state
conditions persistence is likely to be a good forecast. One could make a post facto calculation of the constant c in equation (2) based on the known initial conditions. Such a procedure would yield impressive values of the correlation coefficient and the mean relative
error, but these values would only be as good as a persistence forecast, not better.
4. F U R T H E R S I M P L I F I C A T I O N
Gifford and Hanna (1973) have introduced a further simplification of their model. They
have tabulated, the total annual pollutant emissions, annual average wind velocities, the
annual average pollutant concentrations and the areas for many cities in the United States.
Assuming that these data should conform to their model, i.e. equation (2), they have computed the constant c for each of the cities from the tabulated values of A', Q and ti. They
then have averaged over these values of c and proposed that equation (2), with the resulting
value of c, gives a general model for predicting urban air pollution. They have carried out
this procedure for two types of pollutants, oxides of sulfur (SOJ and paniculate matter.
Oxides of sulfur
For SOX the resulting equation obtained from data for 20 cities is:
X = 5QQfungm~ 3 .
(4)
The correlation coefficient between A' and Q/u for these 20 cities is 0.15. Now, if two
variables are totally uncorrelated. the probability that a random sample of 20 observations
560
S. HAMI-:KI>
Table 2. Comparison of three formulas, equations (5, 6 and 7X for predicting annual
average paniculate concentration in 29 U.S. cities
Index
Formula
X = 225 Q/u, equation (5)
X = 94 + 22 Q/u. equation (6)
(least squares fit)
X = 11 1, equation (7)
(average value)
Mean relative
error
Standard error
of estimate
0.56
124
0.06
26
0.07
29
5. C O N C L U S I O N S
Generally speaking, the case of Nashville discussed above illustrates that, at least in
some cases, urban air pollution modelling is a complex forecasting problem and simple
considerations like those of equations (1 and 2) are not sufficient to cope with it. As Gifford
and Hanna point out, most current detailed models of urban air pollution predict concentrations with errors, on the average, of the order of a factor of 2. This is because of
the poor quality of data and also because dispersion modelling is still a developing technique. Most of currently available data are such that a prediction better than with an error
of a factor of 2 may be regarded as fortuitous. This does not mean, however, that there
is no need for developing models which take account of the complexities of meteorological,
topographical or of other types, which determine the dispersion of pollutants. If dispersion modelling is to play a useful role in urban planning or in devising pollution control
strategies, it is necessary that reliable models of atmospheric dispersion be available. While
a sophisticated model developed for a particular situation can be depended upon to predict pollution concentration to within a factor of, say. 2 on the average, it is apparent from
considerations discussed above that simple models like equations (1 and 2) or (5) cannot
be relied upon to give results which are always co-rect to within a given margin of error.
Accuracy of detailed dispersion models is likely to increase as more and better data
become available. Moreover, a comprehensive dispersion model for a given location need
to be constructed only once, after which it can be used continuously with updated source
information and a predicted flow field to monitor and simulate the expected pollution
field. It is of course possible that under certain conditions simple models may give results
comparable to more sophisticated methods, but until such conditions are clearly understood and categorized one cannot depend upon the simple models.
Acknowledgements—The author wishes to thank Dr. D. Randerson of the Air Resources Laboratory of the U.S.
Department of Commerce for very useful discussions about this work.
"
#t** G****- /S*f.
33-
REFERENCES
Bevington P. R. (1969) Data Reduction and Error Analysis for the Physical Sciences, pp. 310-312. McGraw-Hill,
New York.
Gifford F. A. and Hanna S. R. (197!) Urban air pollution modelling. Proceedings of The 2nd International Clean
Air Congress (Edited by Englund H. M. and Beery \V. T.). pp. 1146-1151.
Gilford F. A. and Hanna S. R. (1973) Modelling urban air pollution. Atmospheric Environment 7, 131-136.
Halliday E. C. and Ventner G. (1971) A numerical experiment in simulating the transport of sulfur dioxide
thrnueh the atmosphere. Atmospheric Environment 5, 815-8IS.
Hamced S. (1974) A multi-cell method for simulation of atmospheric transport. Atmospheric Environment, to be
published.
Modelling urban air pollution
1
-4
S61
Miller M. E. and Holzworth G. C. (1967) An atmospheric diffusion model for metropolitan areas. J. Air Pollut.
Control Ass. 17,46-50.
Randerson D. (1968) A numerical model for predicting the transport of sulfur dioxide through the atmosphere.
Ph.D. dissertation, Texas A & M University, 153 pp.
Randerson D. (1970) A numerical experiment in simulating the transport of sulfur dioxide through the atmosphere. Almosplieric Environment 4, 615-632.
Smith M. (1961) The concentrations and residence times of pollutants in the atmosphere. Chemical Reactions
in the Lower and Upper Atmosphere, pp. 155-166. Interscience, New York.
Stalker W.W.. Kenline P: A. and Paulus H. J.( 1964) Nashville sulfurdioxide emission inventory and the relationship to measured sulfur dioxide. J. Air Pollut. Control Ass. 14, 469-474.